The position $(x)$ of a particle moving along the $x$-axis varies with time $(t)$ as shown in the figure. The average acceleration of the particle in the time interval $t=0$ to $t=8 \, s$ is ........... $m/s^2$.

Draw the $x-t$ graph for positive acceleration.

$A$ bullet is shot vertically downwards with an initial velocity of $100\,m/s$ from a certain height. Within $10\,s$,the bullet reaches the ground and instantaneously comes to rest due to a perfectly inelastic collision. The velocity-time curve for the total time $t = 20\,s$ will be: (Take $g = 10\,m/s^2$)

The velocity-time $(v-t)$ graph for a moving object is shown in the figure. The total displacement of the object during the time interval when there is non-zero acceleration and retardation is ........ $m$.

Given below are two statements:
Statement $I:$ Area under velocity-time graph gives the displacement of the body in a given time.
Statement $II:$ Area under acceleration-time graph is equal to the change in velocity in the given time.
In the light of given statements,choose the correct answer from the options given below.

The relation between velocity $v$ and displacement $x$ is $v = x^2$. Find the acceleration at $x = 3 \ m$.